solve this (1.05)^n=2?

(1.05)^n=2
ln(1.05^n) = ln(2)
n*ln(1.05) = ln(2)
n=ln(2)/ln(1.05)
n=0.69314718055994530941723212145818 / 0.048790164169432003065374404223165
n=14.206699082890474130320233631901

This is a logarithm problem. The equation can be rewritten as:

log 1.05 (2) = n

That's the log of 2 with a base of 1.05. Take the log of 2 with any base, and divide by the log of 1.05 in that same base. Using a regular base 10 log:

log(2) / log(1.05) = n

If you run that through a calculator you'll get about 14.21.

If you don't have a way to get the log base 10, you can use the natural log the same way:

ln(2) / ln(1.05) = n

The answer is the same both ways.

If you do not know how to use logarithms yet, you can still solve this using a graphing calculator. Just remember that this problem is asking you what power you would have to raise 1.06 to in order to get an answer of 2. Just graph y=(1.06)^x. This will show you a graph of all the powers of 1.06. Just find when the y value hits 2 and see what x value this matches up with.

Note: You might have to adjust the scale of the calculator for some problems to make the x or y axis display the range you are seeking.

n log 1.05 = log 2

n = log 2 / log 1.05

n = 14.2 ( any log base may be used )

1.05^n = 2
log(1.05^n) = log(2)
n[log(1.05)] = log(2)
n = log(2)/[log(1.05)]
n = 14.21

( 1.05 ) ^ n = 2
Taking log on both sides,
=> n x log ( 1.05 ) = log ( 2 )
=> n = log ( 2 ) / log ( 1.05 )
=> n = 14.207

(1.05)^n=2
take the log of both sides
n (log(1.05)) = log 2
n = log 2/log(1.05)= 0.30103/0.021189= 14.2067
n = 14.2067

1.05=(2)^(1/n)
=>log 1.05 =(1/n) => log1.05/log2 =(1/n)
2
=>n=14.027

(1.05) ⁿ=2
taking log on both sides we get
log(1.05)ⁿ =log2
→n log1.05=log2
hence n =log2/log1.05≈14.207

Answer = 14.207

( 1.05 ) ^ n = 2
Taking log on both sides,
=> n x log ( 1.05 ) = log ( 2 )
=> n = log ( 2 ) / log ( 1.05 )
=> n = 14.207

n=2/1.05=1.90476